One important design feature with band beans is shear at the supports. With your beams wider than your columns, a conventional one way shear check on the whole cross section is inadequate. You get a shear situation that more resembles punching shear.
This is a very popular system in my area for below grade parking structures. I may disagree with with one of the disadvantages listed above. Wide beams accommodate vertical penetrations relatively easily and I consider that a benefit of the system.
I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.